ON THE GEOMETRIC DEPENDENCE OF RIEMANNIAN SOBOLEV BEST CONSTANTS

被引：2

作者：

Barbosa, Ezequiel R. ^{[1
]}

Montenegro, Marcos ^{[1
]}

机构：

[1] Univ Fed Minas Gerais, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 06期

关键词：

sharp Sobolev inequalities; extremal functions; compactness; unifomity problem; ISOPERIMETRIC-INEQUALITIES; COMPACT MANIFOLDS;

D O I：

10.3934/cpaa.2009.8.1759

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We concerns here with the continuity on the geometry of the second Riemannian L(p)-Sobolev best constant B(0)(p, g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B(0)(p, g) depends continuously on g in the C(2)-topology. Moreover, this topology is sharp for p = 2. From this discussion, we deduce some existence and C(0)-compactness results on extremal functions.

引用

页码：1759 / 1777

页数：19

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